There are many circumstances in which the statistical characteristics of a signal need to be analysed, for the purpose of, for example, classification of the signal, or monitoring or prediction of the signal behaviour. As will be described in further detail below, an example in which such determination is useful is that of random number generation, for example for use in cryptography. A random or chaotic noise signal can be applied to a digitiser which samples the signal at predetermined sampling intervals and outputs a digital representation of the signal which constitutes a random number. For efficiency, the sampling interval should be short. However, short sampling intervals may lead to random numbers which are not statistically independent of each other. It would therefore be desirable to analyse the statistical characteristics of the noise signal so as to enable the determination of the minimum sampling interval which is required to produce statistically independent random numbers.
There are many other circumstances in which signal statistics determination is useful. Where the signal represents variations in a physical parameter of a source, the statistical analysis can be used to classify the source. For example, each signal may represent variations within an image, and the statistical assessment can be used to classify the subject of the image. Similarly, statistical analysis could be used for classification of sound, such as speech or music.
Known analysis techniques include frequency-domain (or spectral) methods, and time-domain methods. Time-domain methods are often necessary in order to provide the required information, and are commonly based on autocorrelation of the signal.
Conventional correlation techniques are however based on the implicit assumption that the signal of interest is Gaussian, and that the statistical behaviour of the signal when considered in the forward direction of time corresponds to that in the backwards direction of time; any asymmetry in the behaviour is lost due to the fact that a correlation function is insensitive to the time direction. In practice, many of the signals being monitored are actually non-Gaussian. Non-linear dependencies in such signals may not be detected by standard correlation techniques.
It would therefore be desirable to provide a method and an apparatus for analysing the statistical behaviour of a signal, which provides a more useful result than the prior art techniques.